Bi-layer PMUT: Bimorph Ultrasonic Transducer

• Bi-layer PMUTs are ultrasonic transducers that use two piezoelectric layers arranged to constructively reinforce membrane bending for enhanced electromechanical coupling.
• They employ various material stacks and precise fabrication routes where process parameters like deposition temperature and interlayer adhesion critically affect device yield and performance.
• Demonstrations show that bilayer designs can achieve up to fourfold coupling improvement and broader bandwidth compared to unimorph counterparts, although they may also exhibit reduced quality factor.

Searching arXiv for bilayer/bimorph PMUT literature and the cited review to ground the article. arxiv_search(query="PMUT bilayer bimorph piezoelectric micromachined ultrasonic transducer", max_results=10) A bi-layer piezoelectric micromachined ultrasonic transducer (PMUT), often termed a bimorph PMUT, is a micromachined ultrasonic membrane in which two active piezoelectric films are arranged so that their electrically induced stresses add constructively in flexure. In the thin-film PMUT literature, this architecture sits within a broader field that began nearly 44 years ago with the primitive development of functional piezoelectric thin-film material, and by 2023 there were already three major companies commercializing PMUTs on a bulk scale; the associated know-how was built by more than 70 different centers, research institutes, and agencies spread across 4 different continents (Roy et al., 2023). In bilayer form, the concept spans deposited thin-film stacks such as AlN/AlN and PZT/AlN, as well as periodically poled single-crystal lithium niobate implementations that realize a bimorph without an intermediate metal electrode (Roy et al., 2023, Yao et al., 30 Aug 2025, Chulukhadze et al., 8 Dec 2025).

1. Structural concept and actuation physics

A bilayer PMUT cell typically consists of, from bottom to top, a handle or substrate, an acoustic cavity or passivation region, a bottom electrode, piezoelectric layer #1, a middle floating electrode, piezoelectric layer #2, a top electrode, and passivation or insulation. In this canonical thin-film form, the two active piezoelectric films are separated by an internal electrode, and the stack is engineered so that the piezoelectric response of the two films reinforces membrane bending rather than only thickness deformation (Roy et al., 2023).

The most-studied bilayer PMUT material combinations reported in the review are AlN/AlN, PZT/AlN, AlN/ScAlN, and emerging PZT/ScAlN or PZT/KNN designs. Representative room-temperature constants listed for these films are: PZT $(\sim 52/48)$ with $\epsilon_{33}^{T}=1200$, $d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$, and $c_{11}^{E}=80\,\mathrm{GPa}$; AlN with $\epsilon_{33}^{T}=10$, $d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$, and $c_{11}^{E}=345\,\mathrm{GPa}$; $\mathrm{Sc}_{0.15}\mathrm{AlN}$ with $\epsilon_{33}^{T}=11$, $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$, and $\epsilon_{33}^{T}=1200$0; and KNN with $\epsilon_{33}^{T}=1200$1, $\epsilon_{33}^{T}=1200$2, and $\epsilon_{33}^{T}=1200$3 (Roy et al., 2023). These combinations are used to balance high piezoelectric stress coefficients, low permittivity, CMOS compatibility, and lead-free or doped material objectives.

Single-crystal lithium niobate bimorphs instantiate the same flexural principle through a different field topology. In the reported X-cut LN device, the active membrane is a trilayer composed of 10 $\epsilon_{33}^{T}=1200$4m X-cut LN, 400 nm SiO$\epsilon_{33}^{T}=1200$5, and 10 $\epsilon_{33}^{T}=1200$6m X-cut LN, with the bottom LN rotated $\epsilon_{33}^{T}=1200$7 in-plane relative to the top LN. Two interleaved platinum electrode pairs on the membrane top drive an in-plane electric field $\epsilon_{33}^{T}=1200$8. Because the bottom LN layer’s Z-axis is inverted, the lateral field induces in-plane stress of opposite sign in the two piezo layers; these opposite stresses add constructively in the out-of-plane direction, while high-order overtone stresses cancel, yielding a pure first-bending resonance (Yao et al., 30 Aug 2025).

The actuation law in that lateral-field LN configuration is expressed as

$\epsilon_{33}^{T}=1200$9

where $d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$0 is in-plane stress. The data report $d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$1 for X-cut LN, and the resulting tensile stress in one layer and compressive stress in the other jointly drive the membrane upward in its fundamental flexural mode (Yao et al., 30 Aug 2025). This establishes a central distinction within the bi-layer PMUT literature: bimorph action does not require a unique electrode topology, only a polarization and field configuration that creates reinforcing bending moments.

2. Fabrication routes and process sensitivities

For deposited thin-film bilayer PMUTs on Si or SOI, a typical fabrication flow is: define and etch the silicon cavity by DRIE or wet etch; deposit and pattern the bottom electrode, such as Ti 5 nm/Pt 100 nm; deposit the first piezo layer by sol–gel PZT, RF magnetron sputtered PZT, or reactive DC sputtered AlN/ScAlN; pattern or etch the first piezo layer; deposit and pattern the middle electrode; deposit the second piezo layer, often at reduced temperature below $d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$2 to avoid interdiffusion; deposit and pattern the top electrode; passivate with PECVD SiO$d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$3 or Parylene-C and open contact vias; and finally release the cavity by backside DRIE or wet etch (Roy et al., 2023).

The same review identifies the critical process parameters that dominate bilayer yield and reproducibility. Deposition temperature influences film crystallinity and residual stress $d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$4; oxygen partial pressure in PZT controls stoichiometry and $d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$5; scandium content in ScAlN tunes $d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$6 and dielectric loss; annealing ramp rates that are too rapid lead to cracking, whereas rates that are too slow reduce throughput; interlayer adhesion is often aided by seed or buffer layers such as TiO$d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$7 and SiO$d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$8; and residual strain matching is designed by tuning the thickness and stress of each film (Roy et al., 2023). These are not peripheral process details: the bilayer concept intensifies sensitivity to stress balance because the desired response is bending rather than only local piezoelectric strain.

Transferred lithium niobate bimorphs follow a different route. One reported implementation starts from a LiNbO$d_{31}=-140\times10^{-12}\,\mathrm{C/m^2}$9–SiO$c_{11}^{E}=80\,\mathrm{GPa}$0–Si wafer containing two single-crystal X-cut LN layers, each 10 $c_{11}^{E}=80\,\mathrm{GPa}$1m thick, with a 400 nm SiO$c_{11}^{E}=80\,\mathrm{GPa}$2 bonding layer; the bottom LN sheet is pre-rotated in-plane by $c_{11}^{E}=80\,\mathrm{GPa}$3 relative to the top to form a periodically poled piezoelectric film stack. Then 100 nm Pt electrodes are patterned on the top LN via lift-off, the wafer is flipped, the silicon substrate is thinned by backside DRIE stopping on buried SiO$c_{11}^{E}=80\,\mathrm{GPa}$4, and a $c_{11}^{E}=80\,\mathrm{GPa}$5 cavity is opened beneath the trilayer so that the LN/SiO$c_{11}^{E}=80\,\mathrm{GPa}$6/LN membrane is free to vibrate. A slight lithography misalignment between the etch and electrode windows shifts the effective diaphragm dimensions and causes a minor resonance down-shift (Yao et al., 30 Aug 2025).

A later P3F LN implementation begins with a 20 $c_{11}^{E}=80\,\mathrm{GPa}$7m P3F LN/400 nm SiO$c_{11}^{E}=80\,\mathrm{GPa}$8/200 $c_{11}^{E}=80\,\mathrm{GPa}$9m Si die of size $\epsilon_{33}^{T}=10$0, forms top electrodes by photolithography and e-beam evaporation of Ti/Pt/Au $\epsilon_{33}^{T}=10$1, deposits 400 nm PECVD SiO$\epsilon_{33}^{T}=10$2 as a hard mask or protective layer, uses DRIE through Si to release the LN membrane, removes sacrificial SiO$\epsilon_{33}^{T}=10$3 by BOE, and optionally packages the device by epoxy attach to PCB, wire-bonding, and open-air anneal at $\epsilon_{33}^{T}=10$4 (Chulukhadze et al., 8 Dec 2025). In this platform, the P3F construction uses two LN films bonded with $\epsilon_{33}^{T}=10$5 flipped crystal orientation, so no intermediate electrode is required (Chulukhadze et al., 8 Dec 2025). A common misconception is therefore that every bilayer PMUT must contain a metal electrode between piezoelectric layers; the P3F LN architecture is an explicit counterexample.

3. Governing equations and modeling frameworks

Bi-layer PMUT analysis in the cited modeling work is formulated in the small-strain, linear piezoelectric regime. With mechanical displacement vector $\epsilon_{33}^{T}=10$6, strain tensor $\epsilon_{33}^{T}=10$7, electric field $\epsilon_{33}^{T}=10$8, Cauchy stress $\epsilon_{33}^{T}=10$9, and electric displacement $d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$0, the constitutive stress–charge relations are

$d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$1

$d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$2

supplemented by equilibrium and Gauss’s law,

$d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$3

For composite bi-layer structures, the interface conditions on the bonded surface enforce displacement continuity, traction continuity, electric potential continuity, and charge continuity (Bolborici et al., 2011). This formulation is sufficiently general to cover piezoelectric–substrate composites and bilayer piezoelectric stacks.

The finite-volume treatment partitions the domain into control volumes and integrates equilibrium and Gauss’s law over each cell. The resulting surface-flux balances produce a sparse nodal circuit network in which local mechanical contributions map to mass–spring elements and local electrical contributions to capacitances, while piezoelectric coupling yields controlled sources between mechanical and electrical circuits (Bolborici et al., 2011). This circuit interpretation parallels equivalent-circuit PMUT design methods used elsewhere in the literature, including Mason and modified Butterworth–Van Dyke extractions (Narvaez et al., 2021, Chulukhadze et al., 8 Dec 2025).

For bilayer PMUTs specifically, the review gives an energy-based thickness-mode coupling factor

$d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$4

with

$d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$5

$d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$6

In the symmetric bimorph case, where $d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$7 and thickness are equal, $d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$8 doubles compared to a single layer (Roy et al., 2023). This directly explains why bilayer actuation can deliver higher coupling and stronger bending moments than unimorph operation.

For flexural resonance, the reported closed-form relation for a clamped circular plate of radius $d_{31}=-2.5\times10^{-12}\,\mathrm{C/m^2}$9 and total thickness $c_{11}^{E}=345\,\mathrm{GPa}$0 is

$c_{11}^{E}=345\,\mathrm{GPa}$1

where

$c_{11}^{E}=345\,\mathrm{GPa}$2

and $c_{11}^{E}=345\,\mathrm{GPa}$3 is the first Bessel-root constant for a clamped plate (Yao et al., 30 Aug 2025). In PMUT system design based on equivalent circuits, the effective electromechanical coupling has also been expressed as

$c_{11}^{E}=345\,\mathrm{GPa}$4

with electrode-coverage optimization yielding $c_{11}^{E}=345\,\mathrm{GPa}$5 in the cited circular-cell design methodology (Narvaez et al., 2021). A plausible implication is that bilayer PMUT design is most effective when material selection, geometry, electrode coverage, and extraction model are treated as a coupled problem rather than as independent choices.

4. Performance metrics and representative demonstrations

A representative unimorph-versus-bimorph AlN comparison reported in the review shows the scale of the bilayer effect. The unimorph AlN PMUT has effective $c_{11}^{E}=345\,\mathrm{GPa}$6, resonant frequency $c_{11}^{E}=345\,\mathrm{GPa}$7, $c_{11}^{E}=345\,\mathrm{GPa}$8 bandwidth in water of $c_{11}^{E}=345\,\mathrm{GPa}$9 of $\mathrm{Sc}_{0.15}\mathrm{AlN}$0, transmit sensitivity of $\mathrm{Sc}_{0.15}\mathrm{AlN}$1 at 1 mm, receive sensitivity of $\mathrm{Sc}_{0.15}\mathrm{AlN}$2, and quality factor $\mathrm{Sc}_{0.15}\mathrm{AlN}$3. The corresponding bimorph AlN PMUT has effective $\mathrm{Sc}_{0.15}\mathrm{AlN}$4, resonant frequency $\mathrm{Sc}_{0.15}\mathrm{AlN}$5, bandwidth $\mathrm{Sc}_{0.15}\mathrm{AlN}$6, transmit sensitivity $\mathrm{Sc}_{0.15}\mathrm{AlN}$7 at 1 mm, receive sensitivity $\mathrm{Sc}_{0.15}\mathrm{AlN}$8, and $\mathrm{Sc}_{0.15}\mathrm{AlN}$9 (Roy et al., 2023). The same discussion attributes the changes to roughly fourfold coupling enhancement, stronger bending moment from two layers, broader bandwidth as coupling rises, modest $\epsilon_{33}^{T}=11$0 reduction, possible mode-shape shifts, and a tendency for resonant frequency to down-shift because of added mass and lower effective rigidity per unit thickness (Roy et al., 2023).

The first reported bilayer X-cut LN PMUT prototype demonstrates an out-of-plane mode near 1 MHz with electromechanical coupling of $\epsilon_{33}^{T}=11$1. From the COMSOL admittance, the reported series resonance is $\epsilon_{33}^{T}=11$2 and the parallel resonance is $\epsilon_{33}^{T}=11$3, giving

$\epsilon_{33}^{T}=11$4

Laser Doppler vibrometry shows a peak center displacement of approximately $\epsilon_{33}^{T}=11$5 at $\epsilon_{33}^{T}=11$6. Using $\epsilon_{33}^{T}=11$7 and the LN/SiO$\epsilon_{33}^{T}=11$8/LN laminate properties, finite-element analysis predicts $\epsilon_{33}^{T}=11$9 and a displacement of $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$0 near resonance; the measured resonance is down-shifted to $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$1, and the lower measured displacement is attributed to feedthrough parasitics, electrode mass loading, and slight dimension shifts (Yao et al., 30 Aug 2025).

Subsequent P3F LN bimorph PMUTs improve the extracted flexural-mode coupling and demonstrate harsher-environment operation. In the optimized membrane-geometry study, the reported device exhibits a $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$2 flexural mode, quality factor $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$3 in air after packaging and $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$4 anneal, extracted $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$5 from an mBVD fit, and measured peak displacement $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$6 at $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$7. The same study reports open-circuit receive sensitivity $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$8 and normalized $d_{31}=-3.8\times10^{-12}\,\mathrm{C/m^2}$9, with parasitic feedthrough modeled as series $\epsilon_{33}^{T}=1200$00 and $\epsilon_{33}^{T}=1200$01 (Chulukhadze et al., 8 Dec 2025). These values were obtained after a design workflow that swept crystallographic orientation, membrane shape, and electrode geometry; the chosen geometry for a 1 MHz target used $\epsilon_{33}^{T}=1200$02, $\epsilon_{33}^{T}=1200$03, $\epsilon_{33}^{T}=1200$04, $\epsilon_{33}^{T}=1200$05, and aspect ratio $\epsilon_{33}^{T}=1200$06 (Chulukhadze et al., 8 Dec 2025).

The material-comparison table in that same work places X-cut LN at $\epsilon_{33}^{T}=1200$07, $\epsilon_{33}^{T}=1200$08, $\epsilon_{33}^{T}=1200$09, and Curie temperature $\epsilon_{33}^{T}=1200$10, in contrast to PZT-5A, AlN, and 36\% ScAlN values listed in the same table (Chulukhadze et al., 8 Dec 2025). The paper states that LN offers moderate $\epsilon_{33}^{T}=1200$11, low $\epsilon_{33}^{T}=1200$12, high $\epsilon_{33}^{T}=1200$13, and high Curie temperature, striking a balance between PZT and AlN (Chulukhadze et al., 8 Dec 2025). Within the data provided, this is the clearest materials-based motivation for recent LN bimorph PMUT research.

5. Application domains and system-level design

The review lists several application cases for bilayer PMUTs. Bimorph AlN arrays are reported for high-power in-air rangefinding, generating more than 1 m range with less than 10 Vpp drive. PZT/AlN stacks are described for CMOS-compatible imaging, combining high $\epsilon_{33}^{T}=1200$14 transmit and AlN receive in monolithic integration with ASICs. Enhanced coupling is also linked to fingerprint sensing, where the data specifically mention Qualcomm’s dual-piezo layer “3D Sonic Sensor” as an example in which reduced voltage and increased SNR follow from the bilayer architecture (Roy et al., 2023).

The optimized P3F LN work expands that application space toward harsh environments and mechanically robust, thicker active layers. The potential application spaces listed there are airborne and liquid-coupled ultrasound imaging requiring high transmit efficiency and sensitivity, high-temperature sensing for downhole oil, turbines, and aerospace above $\epsilon_{33}^{T}=1200$15, range-finding and gesture-sensing with thick robust PMUT arrays, integrated MEMS microphones for harsh environments, and bimorph LN transformers and power conversion elements leveraging high $\epsilon_{33}^{T}=1200$16 (Chulukhadze et al., 8 Dec 2025). Because the architecture removes the intermediate electrode and uses a 20 $\epsilon_{33}^{T}=1200$17m single-crystal active layer, the same work emphasizes high power handling and robust packaging as practical consequences of the material platform (Chulukhadze et al., 8 Dec 2025).

PMUT system design literature also shows how membrane-level figures of merit propagate into array and application constraints. In the PMUT-based ultrasonic power-transfer design for brain implants, a cell with radius $\epsilon_{33}^{T}=1200$18, 5 $\epsilon_{33}^{T}=1200$19m PZT, and 10 $\epsilon_{33}^{T}=1200$20m Si was found to have an effective coupling coefficient of $\epsilon_{33}^{T}=1200$21 under clamped-edge boundary conditions and resonance at $\epsilon_{33}^{T}=1200$22. The designed array consisted of $\epsilon_{33}^{T}=1200$23 cells in an area of $\epsilon_{33}^{T}=1200$24, with peak intensity at $\epsilon_{33}^{T}=1200$25 in the near field; to reach an acoustic intensity of $\epsilon_{33}^{T}=1200$26, the reported drive voltage was approximately $\epsilon_{33}^{T}=1200$27 (Narvaez et al., 2021). Although this is not a bilayer piezoelectric stack in the same sense as bimorph AlN or P3F LN, it shows that coupling-factor optimization, mutual impedance, and Rayleigh-length constraints are central to PMUT deployment at the array level.

6. Limitations, misconceptions, and research directions

The current literature does not present bilayer PMUTs as uniformly superior in every metric. In the review’s AlN comparison, the bimorph improves coupling, transmit sensitivity, receive sensitivity, and bandwidth, but the quality factor drops from 45 to 32 (Roy et al., 2023). This directly counters the simplified assumption that a second active layer produces only gains. The same source notes possible mode-shape shifts and resonant-frequency down-shift, while the LN studies show that feedthrough parasitics, electrode mass loading, lithography misalignment, and lateral over-etch can all perturb the measured response away from the nominal finite-element design point (Roy et al., 2023, Yao et al., 30 Aug 2025, Chulukhadze et al., 8 Dec 2025).

A second recurring misconception is that bilayer PMUTs are necessarily fabricated by sequential thin-film deposition with a middle electrode. That is true for many PZT-, AlN-, and ScAlN-based bimorphs, but the P3F LN platform explicitly forms a bimorph without metal between the two LN layers by using opposite piezoelectric polarization generated through $\epsilon_{33}^{T}=1200$28 crystal orientation flip and wafer bonding (Chulukhadze et al., 8 Dec 2025). This suggests that “bilayer PMUT” is best understood as an electromechanical function rather than a single process recipe.

The main research directions named in the cited works are concrete. The thin-film review forecasts new material stacks such as AlN/ScAlN bilayers to push $\epsilon_{33}^{T}=1200$29 above $\epsilon_{33}^{T}=1200$30 while keeping $\epsilon_{33}^{T}=1200$31 low, identifies thermal-budget management and stress-compensation schemes as integration challenges, and points to flexible or stretchable bilayers combining polymer P(VDF-TrFE) with thin AlN, as well as multimode bilayers for ultra-broadband photoacoustic imaging and on-chip beam steering (Roy et al., 2023). The first LN prototype calls for theoretical analysis, modeling of the measured data, improvement of the transducer topology, and mitigation of feedthrough effects (Yao et al., 30 Aug 2025). The later P3F LN work specifies packaging-free architectures or wafer-scale bonding to improve spurious suppression, material engineering to minimize parasitics and further increase $\epsilon_{33}^{T}=1200$32, and system-level integration in high-temperature and high-frequency wireless front ends (Chulukhadze et al., 8 Dec 2025).

The thermal data on LN also reshape the design space for bilayer PMUTs. The optimized P3F LN device shows stable frequency and normalized displacement from room temperature up to $\epsilon_{33}^{T}=1200$33, a measured temperature coefficient of frequency of $\epsilon_{33}^{T}=1200$34, survival at $\epsilon_{33}^{T}=1200$35 for 1 h, and failure near $\epsilon_{33}^{T}=1200$36 as Au electrodes diffuse and the Si substrate cracks (Chulukhadze et al., 8 Dec 2025). A plausible implication is that the principal bottlenecks in extreme-temperature PMUT operation may shift from the piezoelectric crystal itself to electrodes, substrates, encapsulants, and package-induced boundary conditions. In that sense, bi-layer PMUT research increasingly couples material science, MEMS process control, and electromechanical modeling rather than treating them as separable problems.